if x be real number such that x^3+4x=8 then value of x^7+64x^2=?

Hello student,
Please find the answer to your question below
(x^3 + 4x)^2 = 8^2
=> x^6 + 16x^2 + 8x^4 = 64;
Multiply both sides by x
=> x^7 + 16x^3 + 8x^5 = 64x;
Add 16x^3 in both sides
=> x^7 + 8x^5 + 32x^3 = 16x^3 + 64x;
=> x^7 + 8x^2(x^3 + 4x) = 16(x^3 + 4x);
=> x^7 + 8x^2 * 8 = 16 * 8;
=> x^7 + 64x^2 = 128 .